Question

there is a triangle with side a labeled 32, side b labeled 30, and side c. the formula $a^2 + b^2 = c^2$ is written, followed by $32^2 + 30^2 = $ and $1024 + 900 = $

Explanation:

Step1: Identify right triangle sides

Let $a=32$, $b=20$, find hypotenuse $c$.

Step2: Apply Pythagorean theorem

$$c^2 = a^2 + b^2$$

Step3: Calculate squared side values

$32^2 = 1024$, $20^2 = 400$

Step4: Sum squared values

$$c^2 = 1024 + 400 = 1424$$

Step5: Solve for $c$

$$c = \sqrt{1424} = \sqrt{16 \times 89} = 4\sqrt{89} \approx 37.749$$

Answer:

$4\sqrt{89}$ (or approximately 37.75)